%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----

close all; clc; clear all; 

addpath('../../BookCode');

h = 2;

y0 = 50;
k = 0.05;
y_truth = @(t) ( y0*exp(-k*t) );

fprime = @(t,y) ( -k * y );

[tvals, yvals] = abm( fprime, [0,50], y0, h ); v_1 = yvals(end); 
relative_error = ( yvals - y_truth(tvals) ) ./ y_truth(tvals);
ph_abm = plot( tvals, relative_error, '-r' ); hold('on');

[tvals, yvals] = fhamming( fprime, [0,50], y0, h ); v_2 = yvals(end); 
relative_error = ( yvals - y_truth(tvals) ) ./ y_truth(tvals);
ph_hamming = plot( tvals, relative_error, '-k' );

[ v_1, v_2, y_truth(50) ]

legend( [ph_abm,ph_hamming], 'ABM h=2', 'Hamming h=2', 'location', 'southwest' );
xlabel('time'); ylabel('y(t)');
grid('on'); 

%saveas( gcf, '../../WriteUp/Graphics/Chapter5/c_5_p_3_plot.eps', 'epsc' );